A degeneration of stable morphisms and relative stable morphisms

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dc.creatorLi, Jun
dc.date2000-09-09
dc.date2001-04-15
dc.date.accessioned2026-07-07T06:35:21Z
dc.date.available2026-07-07T06:35:21Z
dc.descriptionThe introduction is modified in the revised version. Also, many typos and errors were corrected. Let $W\to C$ be degeneration of smooth varieties so that the special fiber has normal crossing singularity. In this paper, we first constructed the stack of expanded degenerations of $W$. We then constructed the moduli space of stable morphisms to this stack, which provides a degeneration of the moduli spaces of stable morphisms associated to $W/C$. Using similar technique, for a pair of smooth variety and a smooth divisor $(Z,D)$, we constructed the stack of expanded relative pairs and then the moduli spaces of relative stable morphisms to $(Z,D)$. In the subsequent paper we will construct the relative Gromov-Witten invariants and prove a degeneration formula of Gromov-Witten invariants.
dc.description48 pages
dc.identifierhttps://arxiv.org/abs/math/0009097
dc.identifierhttp://arxiv.org/abs/math/0009097
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99769
dc.subjectAlgebraic Geometry
dc.subjectMathematical Physics
dc.titleA degeneration of stable morphisms and relative stable morphisms
dc.typetext

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